2018 AIME II Problems/Problem 6

Problem

A real number $a$ is chosen randomly and uniformly from the interval $[-20, 18]$ . The probability that the roots of the polynomial

$x^4 + 2ax^3 + (2a - 2)x^2 + (-4a + 3)x - 2$

are all real can be written in the form $\dfrac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .

2018 AIME II (Problems • Answer Key • Resources)
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